He's always been a single cat. He's got the run of the house. One food bowl, one water dish—all his. No competition for lap time. No squabbles at the litter box or the scratch pad.

But then you start to worry: I work such long hours. Mittens must get lonely.

Mittens, of course, cannot offer his opinion on this matter. And one day you come home with a new cat from the shelter, and Mittens encounters a creature who looks a lot like him, right here, right now, in his face. Smelling funny! Invading his territory! Taking valuable resources!

While some cats simply don't enjoy the company of their own kind, even those who do can take time to warm up to newcomers.

Grrr! Hiss! Swipe!

Well, it doesn't have to be this way.

Chances are that you didn't bring home your cat's sworn enemy from a previous life: You just failed to consider the situation from a feline perspective.

Unlike dogs, cats are not pack animals, says Molly Stone, animal behavior specialist at the SPCA of Wake County, N.C. While some cats simply don't enjoy the company of their own kind, even those who do can take time to warm up to newcomers.

Whether you're searching for a buddy for a single cat or expanding your feline fiefdom, keep reasonable expectations and plan to do gradual introductions. You can't ensure that the new housemates will love each other, but you can increase the chance of peaceful coexistence.

Mixing and Matching

When it comes to matching cats, there are plenty of theories but no surefire, hard-and-fast rules. "The most common questions I get are, 'Are kittens better than adults?' 'Are males better than females?' 'Is it worse to get two females vs. two males?' " says Ami Manivong of the Humane Society of the Pikes Peak Region in Colorado. "And I tell everyone, 'Cats are different. I can't tell you that two females are going to do worse than two males.' "

Making good matches "is an inexact science … with a good sprinkling of art mixed in," says Stone. Generally, two cats with similar personalities and play styles will get along better than cats whose styles are vastly different. Cats of opposite genders sometimes gel better than same-gender pairs, and older cats tend to cut kittens more slack, so a possible rule of thumb would be to home in on a younger cat of the opposite gender. But the problem with sticking to rules, Stone adds, is that cats haven't actually read any of them.

Cats are different. I can't tell you that two females are going to do worse than two males.” - Ami Manivong

Gretchen Pressley of Colorado knew that finding a match for her alpha female would be tricky. Isabelle had grown up with her littermate, Nico, and while she didn't prefer feline companionship, Pressley says, she liked "having someone to boss around." In March 2013, when Nico was diagnosed with lymphoma, Pressley sought a new cat, both for herself and to keep Isabelle company after Nico died.

As a communications specialist at the Humane Society of the Pikes Peak Region, Pressley got to survey the incoming felines for potential partners. "I needed a cat that was really mellow, that would let her take control, that wouldn't hiss back if she hissed at him," she says. Eventually, she decided to foster a shy white cat named Tanner.

After a slow, structured introduction, Tanner showed Isabelle that he understood she's the boss—he'd hang out in the corner of a room, for example, which Pressley says was perfect for Isabelle. "She didn't really like him, but she tolerated him."

When Nico died last June, Isabelle grew more accepting of Tanner, and Pressley adopted him. While they're not the bonded pair that Isabelle and Nico were, they'll talk to each other and play on the floor, and each seems to be glad the other one is there.

Tanner's personality helped ensure a successful pairing, but Pressley's patient approach was also crucial. "You really just can't give up in the first week and say, 'Oh, they're never gonna like each other,' " she says.

Success by Degrees

Sometimes we choose our pets, and sometimes they're thrust upon us. When you don't have the luxury of choosing a new cat based on your resident cat's personality, a patient approach is even more important.

Longtime feline rescuer Abby Volin regularly brought fosters into her New York studio apartment, so her own cats, Foxy and Portia, were accustomed to strangers. But her boyfriend Max Polonsky's cat, Julia—an only cat for her entire life—posed a challenge. In August 2011, Julia spent a night at Volin's apartment.

"She was growling and hissing and hiding. She sounded like a gremlin," recalls Volin, rescue group coordinator for The HSUS. "I was actually scared of her."

So when Volin and Polonsky got an apartment together in Washington, D.C., and merged their feline families, they knew they had to proceed slowly and carefully.

At first they kept Julia in the bedroom, while Foxy and Portia had the run of the rest of the apartment. Julia hid under the bed for the first three weeks. Volin and Polonsky gave the cats the space they needed, keeping them apart during the day but letting them mingle at night. Good behavior was rewarded with treats. Eventually, the cats achieved an accord.

Today, while the three cats don't exactly snuggle, they tend to stay in the same room and like keeping an eye on one another.

"They're friends in their own way," Volin says. "I never thought Julia would coexist peacefully and happily with other cats, and now she's one of the gang."

Six-Part Harmony

Since no method of matching cats is foolproof, slow and structured introductions are crucial. Follow these six gradual steps for your best chance of success.

Christina Gandolfo/Alamy

1. Exchange of smells. In the beginning, keep the cats separate, confining the new addition to a small area such as a bathroom for up to a week. Give the newcomer a blanket or pillow that your resident cat has lain on, and exchange the items daily. This will help acclimate your new cat to the smells of her new home and her new housemate.

2. Supervised exploration. Next, put your resident cat in a separate room while letting the new cat investigate other rooms. Keep some doors closed so the cat isn’t overwhelmed and you can control where she goes.

3. Visual introductions. So far so good? Then with one cat confined to a room, crack open the door and let the cats see each other from a comfortable distance as you offer them a meal. Gradually decrease the distance between the feeding bowls and, using a baby gate across the door to keep the cats physically separated, open the door a little wider each time.

Meredith Lee/The HSUS

4. Supervised physical introductions. Once the cats are tolerating the sight of one another, they can meet (at first it might be wise to keep them on harnesses or leashes). Have toys or treats handy that you can use to help each cat associate one another with something positive and to distract them.

6. Solo physical interactions. If all is going well, it’s time to leave the cats alone for gradually longer periods. Start by leaving the house for a few minutes, then increase the amount of time the animals go solo.